Massive Double Copy in the High-Energy Limit

TL;DR

This paper investigates the massive double copy in high-energy regimes, revealing that it requires information beyond the eikonal limit and establishing classical double copy relations for shockwave backgrounds, suggesting a potential all-loop generalization.

Contribution

It extends the understanding of the massive double copy beyond tree-level and high-energy limits, proposing a classical double copy relation for shockwaves and hinting at an all-loop formulation.

Findings

Massive double copy requires data outside the eikonal limit.

A simple phase shift double copy relation is identified.

Classical double copy relation for shockwaves depends on boundary conditions.

Abstract

The exploration of the massive double copy is still in its infancy, and only a few examples in limited contexts are known. In this paper, we analyze the newly discovered double copy for topologically massive theories beyond tree-level amplitudes in the high-energy (eikonal) limit. We find that contrary to the simple double copy relation that occurs in the massless $d\geq4$ case, the massive double copy requires information outside the eikonal limit to give correct results. However, a simple double copy relation arises for the phase shift. Additionally, we relate the eikonal amplitudes to the corresponding shockwave backgrounds and find a classical double copy relation that is manifest only for the appropriate choice of boundary conditions. This analysis hints towards the existence of a topologically massive double copy at all loop orders.